7 ϕ-FEM: An Efficient Simulation Tool Using Simple Meshes for Problems in Structure Mechanics and Heat Transfer
Stéphane Cotin1, Michel Duprez1, Vanessa Lleras2, Alexei Lozinski3*, and Killian Vuillemot1
1 MIMESIS team, Inria Nancy - Grand Est, MLMS team, Université de Strasbourg, France 2 IMAG, Univ Montpellier, CNRS, Montpellier, France 3 Université de Franche-Comté, CNRS, LmB, Besançon, France * Corresponding author
7.1 Introduction
Taking the geometrical complexity into account is one of the major issues in the computational mechanics. Although some spectacular advances in mesh generation have been achieved in recent years, constructing and using the meshes fitting the geometry of, for example, human organs may still be prohibitively expensive in realistic three-dimensional (3D) configurations. Moreover, when the geometry is changing in time or on iterations of an optimization algorithm, the mesh should be frequently adapted, either by complete remeshing (expensive) or by moving the nodes (may lead to a degradation of the mesh quality, impacting the accuracy and the stability of computations).
Geometrically unfitted methods, i.e., the numerical methods using the computational meshes that do not fit the boundary of the domain, and/or the internal interfaces, have been widely investigated in the computational mechanics for decades. Their variants come under the name of immersed boundary (Mittal and Iaccarino, 2005) or fictitious domain (Glowinski et al., 1994) methods. However, ...